%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM295+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:12:06 PM UTC 2026
% Result : Theorem 3.41s 1.49s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 16 unt; 2 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 29 ~; 18 |; 2 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 34 ( 0 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn8) ).
fof(f10,axiom,
rdn_translate(n9,rdn_pos(rdnn(n9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn9) ).
fof(f274,axiom,
rdn_positive_less(rdnn(n8),rdnn(n9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less89) ).
fof(f281,axiom,
! [X0,X1,X2,X3] :
( ( rdn_translate(X0,rdn_pos(X2))
& rdn_translate(X1,rdn_pos(X3))
& rdn_positive_less(X2,X3) )
=> less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_entry_point_pos_pos) ).
fof(f402,conjecture,
? [X0,X1] : less(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',something_less_something) ).
fof(f403,negated_conjecture,
~ ? [X0,X1] : less(X0,X1),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f406,plain,
! [X0,X1] : ~ less(X0,X1),
inference(ennf_transformation,[],[f403]) ).
fof(f415,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_positive_less(X2,X3) ),
inference(ennf_transformation,[],[f281]) ).
fof(f416,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_positive_less(X2,X3) ),
inference(flattening,[],[f415]) ).
fof(f453,plain,
! [X0,X1] : ~ less(X0,X1),
inference(cnf_transformation,[],[f406]) ).
fof(f461,plain,
! [X2,X3,X0,X1] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_positive_less(X2,X3) ),
inference(cnf_transformation,[],[f416]) ).
fof(f534,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(cnf_transformation,[],[f10]) ).
fof(f535,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(cnf_transformation,[],[f9]) ).
fof(f547,plain,
rdn_positive_less(rdnn(n8),rdnn(n9)),
inference(cnf_transformation,[],[f274]) ).
fof(f619,plain,
! [X2,X3,X0,X1] :
( ~ rdn_positive_less(X1,X3)
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[],[f461,f453]) ).
fof(f628,plain,
! [X0,X1] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n9)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n8))) ),
inference(resolution,[],[f619,f547]) ).
fof(f631,definition,
( spl1_3
<=> ! [X1] : ~ rdn_translate(X1,rdn_pos(rdnn(n8))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f632,plain,
( ! [X1] : ~ rdn_translate(X1,rdn_pos(rdnn(n8)))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f634,definition,
( spl1_4
<=> ! [X0] : ~ rdn_translate(X0,rdn_pos(rdnn(n9))) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f635,plain,
( ! [X0] : ~ rdn_translate(X0,rdn_pos(rdnn(n9)))
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f636,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f628,f634,f631]) ).
fof(f669,plain,
( $false
| ~ spl1_3 ),
inference(resolution,[],[f632,f535]) ).
fof(f670,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f669]) ).
fof(f671,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f635,f534]) ).
fof(f672,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f671]) ).
cnf(s2,plain,
( spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f636]) ).
cnf(s11,plain,
~ spl1_3,
inference(sat_conversion,[],[f670]) ).
cnf(s12,plain,
~ spl1_4,
inference(sat_conversion,[],[f672]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s2,s12,s11]) ).
fof(f673,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM295+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 % Computer : n009.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Sun Sep 27 19:29:16 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.44 Running first-order theorem proving
% 0.10/0.44 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.41/1.49 % (2346648)Detected formulas, will run a generic FOF schedule.
% 3.41/1.49 % (2346656)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1189380178:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.41/1.49 % (2346656)Refutation not found, incomplete strategy
% 3.41/1.49 % (2346656)------------------------------
% 3.41/1.49 % (2346656)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.49 % (2346656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.49 % (2346656)CaDiCaL version: 2.1.3
% 3.41/1.49 % (2346656)Termination reason: Refutation not found, incomplete strategy
% 3.41/1.49 % (2346656)Time elapsed: 0.001 s
% 3.41/1.49 % (2346656)Peak memory usage: 87 MB
% 3.41/1.49 % (2346656)Instructions burned: 1 (million)
% 3.41/1.49 % (2346655)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=395802268:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.41/1.49 % (2346659)dis-21_1_sil=8000:lcm=predicate:random_seed=990424394:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.41/1.49 % (2346653)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=496718444:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.41/1.49 % (2346654)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3236600577:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.41/1.49 % (2346658)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=69798957:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.41/1.49 % (2346659)First to succeed.
% 3.41/1.49 % (2346659)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2346648"
% 3.41/1.49 % (2346657)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=895702167:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.41/1.49 % (2346657)Also succeeded, but the first one will report.
% 3.41/1.49 % (2346658)Also succeeded, but the first one will report.
% 3.41/1.49 % (2346656)------------------------------
% 3.41/1.49 % (2346656)------------------------------
% 3.41/1.49 % (2346667)lrs+10_1_sil=8000:sp=occurrence:random_seed=870269282:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.41/1.49 % (2346667)Also succeeded, but the first one will report.
% 3.41/1.49 % (2346659)Refutation found. Thanks to Tanya!
% 3.41/1.49 % SZS status Theorem for theBenchmark
% 3.41/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.49 % (2346659)------------------------------
% 3.41/1.49 % (2346659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.49 % (2346659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.49 % (2346659)CaDiCaL version: 2.1.3
% 3.41/1.49 % (2346659)Termination reason: Refutation
% 3.41/1.49 % (2346659)Time elapsed: 0.007 s
% 3.41/1.49 % (2346659)Peak memory usage: 89 MB
% 3.41/1.49 % (2346659)Instructions burned: 11 (million)
% 3.41/1.49 % (2346659)------------------------------
% 3.41/1.49 % (2346659)------------------------------
% 3.41/1.49 % (2346648)Success in time 0.416 s
% 3.41/1.49 % Vampire exiting
%------------------------------------------------------------------------------